2020欧几里得数学竞赛真题资料 来为4月比赛打基础

即将和新年一起到来的，还有一连串高含金量的国际竞赛，比如AMC、欧几里得、BBO、物理碗等等。我们今天就来分享几道欧几里得数学竞赛真题与答案解析，帮助大家更好地准备利用剩下3个月的复习时间。

（点击查看2022脑科学竞赛时间已官宣，往届多名选手被哈耶普斯录取）

2020欧几里得数学竞赛真题精选

【题目】

8

(a)Four tennis players Alain,Bianca,Chen,and Dave take part in a tournament in
which a total of three matches are plaved. First,two players are chosen randomly to play each other. The other two players also play each other. The winners of the two matches then play to decide the tournament champion, Alain, Bianca and Chen are equally matched (that is, when a match is played between any two of them, the probability that each player wins is s).When Dave plays each of Alain. Bianca and Chen,the probability that Dave wins is p, for some real number p. Determine the probability that Bianca wins the tournament, expressing your answer in the form （ap^2+bp+c）/d

where a, b,c, and d are integers.

(b)Three microphones A,B and C are placed on a line such that A is 1 km west of
BandCis2km east of B.A large explosion occurs at a point P not on this line.Each of the three microphones receives the sound. The sound travels at km/s.Microphone B receives the sound first,microphone A receives the sound s later, and microphone C receives it 1 s after microphone A. Determine the distance from microphone B to the explosion at P.
9
a)AnL shape is made by adjoining three congruent squares. The L is subdivided
into four smaller L shapes,as shown. Each of the resulting L's is subdivided in this same way. After the third round of subdivisions, how many L's of the smallest size are there?

——————欧几里得数学竞赛真题———————

(b)After the third round of subdivisions, how many L's of the smallest size are in
the same orientation as the original L?

(c)Starting with the original L shape,2020 rounds of subdivisions are made.
Determine the number of L's of the smallest size that are in the same orientation as the original L.

【答案】

像欧几里得这类的国际竞赛不像学校里的考试那样，有很多固定的套路，会非常考验你的创造力和灵活的思维能力，如果感觉一个人摸索复习有点孤单，可以点击预约试听【唯寻欧几里得竞赛班课】——

根据学员进度定制课程

介绍联想、类比、归纳、转化、试误等答题技巧

整合大量竞赛全真题库

进行模块化学习

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